Local Regularization Does Not Characterize Multiclass PAC Learnability

תקציר מקורי באנגליתarXiv:2607.23449v1 Announce Type: new Abstract: Local regularization assigns each hypothesis a test-point-dependent score and predicts with a minimum-score hypothesis consistent with the sample. Asilis et al. asked whether this principle characterizes multiclass PAC learnability. We give a negative answer. There is a countable class of Daniely--Shalev-Shwartz dimension at most two with realizable PAC sample complexity \[ O\!\left(\frac{1}{\varepsilon}\log\frac{1}{\delta}\right), \] that no local regularizer learns. Hypotheses are edges of complete graphs and instances are tournaments. At a test tournament, the scores fix an edge ranking while the training sample independently removes competitors. Cyclic triangles force enough inversions that surviving competitors produce constant populatio